{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a11f966d-2b32-462b-af04-6e6497471551",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Minimum Dominating Set (MDS) Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2442c6fd-4985-47f5-b726-4ee0af7852ed",
   "metadata": {
    "tags": []
   },
   "source": [
    "The Minimum Dominating Set problem [[1]](#MDSWiki) is a classical NP-hard problem in computer science and graph theory. In this problem, we are given a graph, and we aim to find the smallest subset of vertices such that every node in the graph is either in the subset or is a neighbor of a node in the subset.\n",
    "\n",
    "We represent the problem as a binary optimization problem.\n",
    "\n",
    "### Variables:\n",
    "\n",
    "- $x_i$ binary variables that represent whether a node $i$ is in the dominating set or not.\n",
    "\n",
    "### Constraints:\n",
    "\n",
    "- Every node $i$ is either in the dominating set or connected to a node in the dominating set:\n",
    "\n",
    "  $\\forall i \\in V: x_i + \\sum_{j \\in N(i)} x_j \\geq 1$\n",
    "\n",
    "  Where $N(i)$ represents the neighbors of node $i$.\n",
    "\n",
    "### Objective\n",
    "\n",
    "- Minimize the size of the dominating set:\n",
    "\n",
    "  $\\sum_{i\\in V}x_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "877ae3cf-10cc-4e51-a428-eb57687d8d18",
   "metadata": {},
   "source": [
    "# Solving with the Classiq platform\n",
    "\n",
    "We go through the steps of solving the problem with the Classiq platform, using QAOA algorithm [[2](#QAOA)]. The solution is based on defining a pyomo model for the optimization problem we would like to solve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "49a9588b-e79e-4813-b7c5-ac068d7b930c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:25.623073Z",
     "iopub.status.busy": "2024-05-07T15:49:25.622600Z",
     "iopub.status.idle": "2024-05-07T15:49:26.563429Z",
     "shell.execute_reply": "2024-05-07T15:49:26.562633Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from typing import cast\n",
    "\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pyomo.core as pyo\n",
    "from IPython.display import Markdown, display\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8517ef73-faf6-4fd8-9db8-4088551398e0",
   "metadata": {},
   "source": [
    "## Building the Pyomo model from a graph input\n",
    "\n",
    "We proceed by defining the pyomo model that will be used on the Classiq platform, using the mathematical formulation defined above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "48889b21-557b-481c-80c5-3c0b5c91adb6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:26.569484Z",
     "iopub.status.busy": "2024-05-07T15:49:26.567691Z",
     "iopub.status.idle": "2024-05-07T15:49:26.575990Z",
     "shell.execute_reply": "2024-05-07T15:49:26.575285Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import pyomo.core as pyo\n",
    "\n",
    "\n",
    "def mds(graph: nx.Graph) -> pyo.ConcreteModel:\n",
    "    model = pyo.ConcreteModel()\n",
    "    model.x = pyo.Var(graph.nodes, domain=pyo.Binary)\n",
    "\n",
    "    @model.Constraint(graph.nodes)\n",
    "    def dominating_rule(model, idx):\n",
    "        sum_of_neighbors = sum(model.x[neighbor] for neighbor in graph.neighbors(idx))\n",
    "        return model.x[idx] + sum_of_neighbors >= 1\n",
    "\n",
    "    model.cost = pyo.Objective(expr=sum(model.x.values()), sense=pyo.minimize)\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffd32c78-9492-4ced-a5a0-9ba61d1b43b7",
   "metadata": {},
   "source": [
    "The model contains:\n",
    "\n",
    "- Index set declarations (model.Nodes, model.Arcs).\n",
    "- Binary variable declaration for each node (model.x) indicating whether that node is chosen for the set.\n",
    "- Constraint rule \u2013 for each node, it must be a part of the chosen set or be neighbored by one.\n",
    "- Objective rule \u2013 the sum of the variables equals the set size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69359e3e-ed85-4b56-9afb-9dd4b9997ada",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:26.580604Z",
     "iopub.status.busy": "2024-05-07T15:49:26.579463Z",
     "iopub.status.idle": "2024-05-07T15:49:27.071051Z",
     "shell.execute_reply": "2024-05-07T15:49:27.070323Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate a random graph\n",
    "G = nx.erdos_renyi_graph(n=6, p=0.6, seed=8)\n",
    "nx.draw_kamada_kawai(G, with_labels=True)\n",
    "\n",
    "mds_model = mds(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4a985b32-0670-42f3-ba50-5c0097eb75f5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:27.075862Z",
     "iopub.status.busy": "2024-05-07T15:49:27.074634Z",
     "iopub.status.idle": "2024-05-07T15:49:27.084010Z",
     "shell.execute_reply": "2024-05-07T15:49:27.083316Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 Set Declarations\n",
      "    dominating_rule_index : Size=1, Index=None, Ordered=False\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    6 : {0, 1, 2, 3, 4, 5}\n",
      "    x_index : Size=1, Index=None, Ordered=False\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    6 : {0, 1, 2, 3, 4, 5}\n",
      "\n",
      "1 Var Declarations\n",
      "    x : Size=6, Index=x_index\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :  None :     1 : False :  True : Binary\n",
      "          1 :     0 :  None :     1 : False :  True : Binary\n",
      "          2 :     0 :  None :     1 : False :  True : Binary\n",
      "          3 :     0 :  None :     1 : False :  True : Binary\n",
      "          4 :     0 :  None :     1 : False :  True : Binary\n",
      "          5 :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "1 Objective Declarations\n",
      "    cost : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Sense    : Expression\n",
      "        None :   True : minimize : x[0] + x[1] + x[2] + x[3] + x[4] + x[5]\n",
      "\n",
      "1 Constraint Declarations\n",
      "    dominating_rule : Size=6, Index=dominating_rule_index, Active=True\n",
      "        Key : Lower : Body                             : Upper : Active\n",
      "          0 :   1.0 :        x[1] + x[3] + x[5] + x[0] :  +Inf :   True\n",
      "          1 :   1.0 :        x[0] + x[2] + x[4] + x[1] :  +Inf :   True\n",
      "          2 :   1.0 : x[1] + x[3] + x[4] + x[5] + x[2] :  +Inf :   True\n",
      "          3 :   1.0 :        x[0] + x[2] + x[4] + x[3] :  +Inf :   True\n",
      "          4 :   1.0 : x[1] + x[2] + x[3] + x[5] + x[4] :  +Inf :   True\n",
      "          5 :   1.0 :        x[0] + x[2] + x[4] + x[5] :  +Inf :   True\n",
      "\n",
      "5 Declarations: x_index x dominating_rule_index dominating_rule cost\n"
     ]
    }
   ],
   "source": [
    "mds_model.pprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17ea14ec-dbb7-487c-b4f1-cabc8d5e3c29",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Setting Up the Classiq Problem Instance\n",
    "\n",
    "In order to solve the Pyomo model defined above, we use the Classiq combinatorial optimization engine. For the quantum part of the QAOA algorithm (`QAOAConfig`) - define the number of repetitions (`num_layers`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "816b468f-a59f-4f2f-8337-4a9d66548425",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:27.088831Z",
     "iopub.status.busy": "2024-05-07T15:49:27.087615Z",
     "iopub.status.idle": "2024-05-07T15:49:29.115837Z",
     "shell.execute_reply": "2024-05-07T15:49:29.115200Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import construct_combinatorial_optimization_model\n",
    "from classiq.applications.combinatorial_optimization import OptimizerConfig, QAOAConfig\n",
    "\n",
    "qaoa_config = QAOAConfig(num_layers=6, penalty_energy=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db34d5ac-6877-4285-8dec-7bf7b37eb783",
   "metadata": {},
   "source": [
    "For the classical optimization part of the QAOA algorithm we define the maximum number of classical iterations (`max_iteration`) and the $\\alpha$-parameter (`alpha_cvar`) for running CVaR-QAOA, an improved variation of the QAOA algorithm [[3](#cvar)]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e41d0dd3-4135-4330-9ba3-c1b30c339a74",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:29.118667Z",
     "iopub.status.busy": "2024-05-07T15:49:29.118296Z",
     "iopub.status.idle": "2024-05-07T15:49:29.121576Z",
     "shell.execute_reply": "2024-05-07T15:49:29.120968Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "optimizer_config = OptimizerConfig(max_iteration=30, alpha_cvar=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "214d6051-43b8-4b9d-8454-f9cdb62b4cf0",
   "metadata": {},
   "source": [
    "Lastly, we load the model, based on the problem and algorithm parameters, which we can use to solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0243019c-6fc3-435f-b6ec-8b4355d6660c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:29.124125Z",
     "iopub.status.busy": "2024-05-07T15:49:29.123766Z",
     "iopub.status.idle": "2024-05-07T15:49:31.641160Z",
     "shell.execute_reply": "2024-05-07T15:49:31.640352Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "qmod = construct_combinatorial_optimization_model(\n",
    "    pyo_model=mds_model,\n",
    "    qaoa_config=qaoa_config,\n",
    "    optimizer_config=optimizer_config,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fcc3812-c9d0-421c-84bb-38047297b33f",
   "metadata": {},
   "source": [
    "We also set the quantum backend we want to execute on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "53bc041f-065c-44d2-b220-dafd9d0504ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:31.645316Z",
     "iopub.status.busy": "2024-05-07T15:49:31.645031Z",
     "iopub.status.idle": "2024-05-07T15:49:31.738219Z",
     "shell.execute_reply": "2024-05-07T15:49:31.737432Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import set_execution_preferences\n",
    "from classiq.execution import ClassiqBackendPreferences, ExecutionPreferences\n",
    "\n",
    "backend_preferences = ExecutionPreferences(\n",
    "    backend_preferences=ClassiqBackendPreferences(backend_name=\"aer_simulator\")\n",
    ")\n",
    "\n",
    "qmod = set_execution_preferences(qmod, backend_preferences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "da54146e-edaa-45e8-8a6a-86b7e24be2a3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:31.743816Z",
     "iopub.status.busy": "2024-05-07T15:49:31.742506Z",
     "iopub.status.idle": "2024-05-07T15:49:31.894435Z",
     "shell.execute_reply": "2024-05-07T15:49:31.893596Z"
    }
   },
   "outputs": [],
   "source": [
    "from classiq import write_qmod\n",
    "\n",
    "write_qmod(qmod, \"minimum_dominating_set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "943291f0-6a9f-4286-a69d-ef13a0a12ef6",
   "metadata": {},
   "source": [
    "## Synthesizing the QAOA Circuit and Solving the Problem\n",
    "\n",
    "We can now synthesize and view the QAOA circuit (ansatz) used to solve the optimization problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1d71e29a-5d53-49c4-84b2-45f59be4da31",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:31.899730Z",
     "iopub.status.busy": "2024-05-07T15:49:31.898448Z",
     "iopub.status.idle": "2024-05-07T15:49:46.574096Z",
     "shell.execute_reply": "2024-05-07T15:49:46.572905Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Opening: https://platform.classiq.io/circuit/d5cb21cc-5e64-4e4e-8ea7-414ea1afd2ee?version=0.41.0.dev39%2B79c8fd0855\n"
     ]
    }
   ],
   "source": [
    "from classiq import show, synthesize\n",
    "\n",
    "qprog = synthesize(qmod)\n",
    "show(qprog)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80238cf9-d7bd-46e5-9d48-b7cf23a6b304",
   "metadata": {},
   "source": [
    "We now solve the problem by calling the `execute` function on the quantum program we have generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "62d12d20-1c80-4a9e-bb6b-b1fddc6cbe40",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:49:46.578242Z",
     "iopub.status.busy": "2024-05-07T15:49:46.577187Z",
     "iopub.status.idle": "2024-05-07T15:52:05.144387Z",
     "shell.execute_reply": "2024-05-07T15:52:05.143772Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import execute\n",
    "\n",
    "res = execute(qprog).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "620ea6a0-cd05-41a9-a2ed-9631c680d2e6",
   "metadata": {},
   "source": [
    "We can check the convergence of the run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "02454398-b229-403c-824a-b1eb539fbc1f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:05.147275Z",
     "iopub.status.busy": "2024-05-07T15:52:05.146690Z",
     "iopub.status.idle": "2024-05-07T15:52:05.166931Z",
     "shell.execute_reply": "2024-05-07T15:52:05.166315Z"
    },
    "tags": []
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=640x480>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from classiq.execution import VQESolverResult\n",
    "\n",
    "vqe_result = res[0].value\n",
    "vqe_result.convergence_graph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "615ed612-b835-4bf0-aa92-92d30ef8006d",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Optimization Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "670eddd3-2da7-4a88-b571-7884ef24f60c",
   "metadata": {},
   "source": [
    "We can also examine the statistics of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "516d78ba-2951-46eb-b1af-efe877513556",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:05.169568Z",
     "iopub.status.busy": "2024-05-07T15:52:05.169098Z",
     "iopub.status.idle": "2024-05-07T15:52:07.389654Z",
     "shell.execute_reply": "2024-05-07T15:52:07.388902Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>cost</th>\n",
       "      <th>solution</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>707</th>\n",
       "      <td>0.001</td>\n",
       "      <td>2.0</td>\n",
       "      <td>[1, 1, 0, 0, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[0, 0, 1, 1, 0, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[1, 1, 0, 1, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>0.001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>[0, 0, 1, 1, 1, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>704</th>\n",
       "      <td>0.001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>[1, 0, 0, 1, 1, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     probability  cost            solution  count\n",
       "707        0.001   2.0  [1, 1, 0, 0, 0, 0]      1\n",
       "482        0.001   3.0  [0, 0, 1, 1, 0, 1]      1\n",
       "158        0.001   3.0  [1, 1, 0, 1, 0, 0]      1\n",
       "121        0.001   4.0  [0, 0, 1, 1, 1, 1]      1\n",
       "704        0.001   4.0  [1, 0, 0, 1, 1, 1]      1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from classiq.applications.combinatorial_optimization import (\n",
    "    get_optimization_solution_from_pyo,\n",
    ")\n",
    "\n",
    "solution = get_optimization_solution_from_pyo(\n",
    "    mds_model, vqe_result=vqe_result, penalty_energy=qaoa_config.penalty_energy\n",
    ")\n",
    "optimization_result = pd.DataFrame.from_records(solution)\n",
    "optimization_result.sort_values(by=\"cost\", ascending=True).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "687f492b-a4a5-49c6-964c-8959b035bb93",
   "metadata": {},
   "source": [
    "And the histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "31a4e74d-b2b8-42e0-826d-de7b51de1fe8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:07.394330Z",
     "iopub.status.busy": "2024-05-07T15:52:07.393146Z",
     "iopub.status.idle": "2024-05-07T15:52:07.701342Z",
     "shell.execute_reply": "2024-05-07T15:52:07.700622Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'cost'}>]], dtype=object)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimization_result.hist(\"cost\", weights=optimization_result[\"probability\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3a890a1-c5d4-409d-b9a3-d7ffd4fdd6c0",
   "metadata": {},
   "source": [
    "Let us plot the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4326e84b-26f6-4ea9-a53b-090fb3658b8c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:07.705568Z",
     "iopub.status.busy": "2024-05-07T15:52:07.704475Z",
     "iopub.status.idle": "2024-05-07T15:52:07.709598Z",
     "shell.execute_reply": "2024-05-07T15:52:07.708959Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "best_solution = optimization_result.solution[optimization_result.cost.idxmin()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3562002f-d425-482d-be71-f9bb36245dc6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:07.713729Z",
     "iopub.status.busy": "2024-05-07T15:52:07.712616Z",
     "iopub.status.idle": "2024-05-07T15:52:08.182072Z",
     "shell.execute_reply": "2024-05-07T15:52:08.181217Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_solution(graph: nx.Graph, solution: list):\n",
    "    solution_nodes = [v for v in graph.nodes if solution[v]]\n",
    "    solution_edges = [\n",
    "        (u, v) for u, v in graph.edges if u in solution_nodes or v in solution_nodes\n",
    "    ]\n",
    "    nx.draw_kamada_kawai(graph, with_labels=True)\n",
    "    nx.draw_kamada_kawai(\n",
    "        graph,\n",
    "        nodelist=solution_nodes,\n",
    "        edgelist=solution_edges,\n",
    "        node_color=\"r\",\n",
    "        edge_color=\"y\",\n",
    "    )\n",
    "\n",
    "\n",
    "draw_solution(G, best_solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dde1905d-aeff-4297-a9d3-ad14910e6161",
   "metadata": {},
   "source": [
    "Lastly, we can compare to the classical solution of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5a7ca4b6-25a0-46dd-b5cc-de6a639a6f57",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:08.194837Z",
     "iopub.status.busy": "2024-05-07T15:52:08.193301Z",
     "iopub.status.idle": "2024-05-07T15:52:08.290328Z",
     "shell.execute_reply": "2024-05-07T15:52:08.289518Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model unknown\n",
      "\n",
      "  Variables:\n",
      "    x : Size=6, Index=x_index\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :   1.0 :     1 : False : False : Binary\n",
      "          1 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          2 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          3 :     0 :   1.0 :     1 : False : False : Binary\n",
      "          4 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          5 :     0 :   0.0 :     1 : False : False : Binary\n",
      "\n",
      "  Objectives:\n",
      "    cost : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Value\n",
      "        None :   True :   2.0\n",
      "\n",
      "  Constraints:\n",
      "    dominating_rule : Size=6\n",
      "        Key : Lower : Body : Upper\n",
      "          0 :   1.0 :  2.0 :  None\n",
      "          1 :   1.0 :  1.0 :  None\n",
      "          2 :   1.0 :  1.0 :  None\n",
      "          3 :   1.0 :  2.0 :  None\n",
      "          4 :   1.0 :  1.0 :  None\n",
      "          5 :   1.0 :  1.0 :  None\n"
     ]
    }
   ],
   "source": [
    "from pyomo.opt import SolverFactory\n",
    "\n",
    "solver = SolverFactory(\"couenne\")\n",
    "solver.solve(mds_model)\n",
    "\n",
    "mds_model.display()\n",
    "classical_solution = [int(pyo.value(mds_model.x[i])) for i in G.nodes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a7524894-b5c5-42d4-8f92-a019bef5e7da",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:08.303277Z",
     "iopub.status.busy": "2024-05-07T15:52:08.302942Z",
     "iopub.status.idle": "2024-05-07T15:52:08.574093Z",
     "shell.execute_reply": "2024-05-07T15:52:08.573365Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_solution(G, classical_solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e82b5953-122a-4707-8ab6-f741f14f13a5",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "tags": []
   },
   "source": [
    "\n",
    "## References\n",
    "\n",
    "<a id='MDSWiki'>[1]</a>: [Dominating Set (Wikipedia)](https://en.wikipedia.org/wiki/Partition_problem)\n",
    "\n",
    "<a id='QAOA'>[2]</a>: [Farhi, Edward, Jeffrey Goldstone, and Sam Gutmann. \"A quantum approximate optimization algorithm.\" arXiv preprint arXiv:1411.4028 (2014).](https://arxiv.org/abs/1411.4028)\n",
    "\n",
    "<a id='cvar'>[3]</a>: [Barkoutsos, Panagiotis Kl, et al. \"Improving variational quantum optimization using CVaR.\" Quantum 4 (2020): 256.](https://arxiv.org/abs/1907.04769)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "vscode": {
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   }
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 },
 "nbformat": 4,
 "nbformat_minor": 5
}
